(4-i)(-7+i)(3i)=

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Solution for (4-i)(-7+i)(3i)= equation: 


Simplifying
(4 + -1i)(-7 + i)(3i) = 0

Remove parenthesis around (3i)
(4 + -1i)(-7 + i) * 3i = 0

Reorder the terms for easier multiplication:
3i(4 + -1i)(-7 + i) = 0

Multiply (4 + -1i) * (-7 + i)
3i(4(-7 + i) + -1i * (-7 + i)) = 0
3i((-7 * 4 + i * 4) + -1i * (-7 + i)) = 0
3i((-28 + 4i) + -1i * (-7 + i)) = 0
3i(-28 + 4i + (-7 * -1i + i * -1i)) = 0
3i(-28 + 4i + (7i + -1i2)) = 0

Combine like terms: 4i + 7i = 11i
3i(-28 + 11i + -1i2) = 0
(-28 * 3i + 11i * 3i + -1i2 * 3i) = 0
(-84i + 33i2 + -3i3) = 0

Solving
-84i + 33i2 + -3i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3i'.
3i(-28 + 11i + -1i2) = 0

Factor a trinomial.
3i((-7 + i)(4 + -1i)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'i' equal to zero and attempt to solve:

Simplifying
i = 0

Solving
i = 0

Move all terms containing i to the left, all other terms to the right.

Simplifying
i = 0

Subproblem 2
Set the factor '(-7 + i)' equal to zero and attempt to solve:

Simplifying
-7 + i = 0

Solving
-7 + i = 0

Move all terms containing i to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + i = 0 + 7

Combine like terms: -7 + 7 = 0
0 + i = 0 + 7
i = 0 + 7

Combine like terms: 0 + 7 = 7
i = 7

Simplifying
i = 7

Subproblem 3
Set the factor '(4 + -1i)' equal to zero and attempt to solve:

Simplifying
4 + -1i = 0

Solving
4 + -1i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1i = 0 + -4
-1i = 0 + -4

Combine like terms: 0 + -4 = -4
-1i = -4

Divide each side by '-1'.
i = 4

Simplifying
i = 4
Solution
i = {0, 7, 4}

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